There have been rumours that Pochettino could leave the club following the exit of executive chairman Nicola Cortese.
On Saturday, he admitted that there were "no guarantees" in football, but The Mirror reports that club owner Katharina Liebherr is ready to give the Argentinian a new contract.
The newspaper quotes a club source as saying that Liebherr is eager for "stability".
"The owner wants some stability at the club and the best way of ensuring this is by getting the manager tied into a contract. It would send out a message that despite Nicola leaving, nothing has changed," the source said.
Pochettino has 17 months left on his current deal.